2.5.4 Analysis of the Concrete Compression Struts

Analysis of the Concrete Compression Struts

To design the concrete compression strut of a shell, it is divided into three surface layers that are subjected to the design membrane forces.

For shells where the applied moment is relatively large in relation to the acting axial force (e_d/h > 0.2), the thickness h_E of the two outer layers is reduced to 0.35 ⋅ d. For shells subjected to approximately concentric compression, the surface layer thickness h_E is increased to half of the plate thickness h. If the related eccentricity of the axial force e_d/h is between 0 and 0.2, the surface layer thickness is interpolated.

For e_d, the larger value among the quotients of m_x/n_x and m_y/n_y is applied.

For the analysis of the concrete compression strut, the concrete strut's compression force to be resisted n_strut,+z is compared with the resistant axial force of the surface layer n_strut,d.

The resistant axial force n_strut,d depends on the thickness h_E of the surface layer and the applied concrete strength f_cd,08.

The first step to determine the thickness of the surface layer is to determine the provided load eccentricities in x- and y-direction from the internal forces of the linear plate analysis:

$e_{dx} = \left|\frac{m_x}{n_x}\right| = \left|\frac{124.35}{- 103.911}\right| = 1.197\text{ m }$

$e_{dy} = \left|\frac{m_y}{n_y}\right| = \left|\frac{54.36}{- 285.386}\right| = 0.190 \text{m}$

The greater load eccentricity in x-direction is computed as governing. It can be used to determine the relative load eccentricity e_d/h.

$\frac{e_d}{h} = \frac{1.197}{1.29} = 0.928 > 0.2$

Since the relative load eccentricity is greater than 0.2, it is a shell that is predominantly subjected to bending. The factor f_hE for determining the surface layer thickness is 0.35.

Thus, the thickness h_E of the surface layer is determined as follows:

$h_E = f_{hE} · h = 0.35 · 129 = 45.15 \text{cm}$

The design value of the concrete compressive strength is reduced to 80 % according to the recommendations of Schlaich/Schäfer (in [2], page 378). This recommendation can also be found in EN 1992-1-1, clause 6.5.2, which regulates the design of compression struts in framework models.

$f_{cd} = \frac{f_{ck}}{{\gamma }_c} = \frac{30}{1.5} = 20 {\text{N/mm}}^{2 }$

$f_{cd,08} = 0.8 · 20 = 16 {\text{N/mm}}^2$

This value can also be found in the design details (see Figure 2.72).

With it, you can determine the resisting force of the concrete compression strut n_strut,d.

• n_strut,d = b ∙ h_E ∙ f_cd,08 = 100 ∙ 45.15 ∙ 16 = 7 224.00 kN/m

The analysis of the concrete compression strut for the top side of the surface is done analogously.